During the drilling of an oil well using rotary drilling techniques, filtrate from the drilling fluid may be forced into the adjacent subterranean formation. In the case of aqueous drilling fluids the filtrate is essentially water, which may have certain undesirable effects on the formation. This invention relates to certain unique polymers which, when dispersed in aqueous drilling fluids, exhibit a superior ability to reduce this tendency of the drilling fluid filtrate to enter the adjacent formation. The polymers of this invention also have excellent calcium tolerance and has excellent thermal stability compared with commercial fluid additives.